Struct easy_ml::differentiation::Record
source · pub struct Record<'a, T: Primitive> {
pub number: T,
pub index: Index,
/* private fields */
}
Expand description
A wrapper around a real number which records it going through the computational graph. This is used to perform Reverse Mode Automatic Differentiation.
§Panics
Every operation and nearly every method a Record has involves manipulating the record’s history on its referenced WengertList. This WengertList itself maintains a RefCell which tracks borrows at runtime rather than compile time. This is neccessary to maintain the illusion that Records are just ordinary numbers, and the side effects of doing arithmetic with Records are limited to their referenced WengertList. Hence, the Rust compiler infers that it is not safe to share references to WengertLists between threads, nor transfer Records across threads. If you called a method on two Records that both mutably borrowed from the same WengertList at once, which could be trivially done with multiple threads, then the code would panic. Easy ML shouldn’t allow you to do this in safe Rust because each mutable borrow of the WengertList is dropped at the end of each Record method call, and you can’t call two methods simulatenously without threading.
§Acknowledgments
A tutorial by Rufflewind and the associated MIT licensed soure code were invaluable in providing understanding on how to implement Reverse Mode Automatic Differentiation.
Fields§
§number: T
The real number
index: Index
The index of this number in its WengertList. The first entry will be 0, the next 1 and so on.
In normal use cases you should not need to read this field, you can index Derivatives directly with Records.
Implementations§
source§impl<'a, T: Numeric + Primitive> Record<'a, T>
impl<'a, T: Numeric + Primitive> Record<'a, T>
The main set of methods for using Record types for Reverse Differentiation.
The general steps are
- create a
WengertList
- create variables from this list
- do operations on the variables
- from the output you want to compute derivatives for call
.derivatives()
- index the
Derivatives
object with the index variables to get the derivatives with respect to each input - if you want to make another pass call
clear()
on theWengertList
and then callreset()
on all of the variables to forget the gradients already computed (the order ofclear
thenreset
is very important!).
Constants can be used to save memory if you have numbers that you do not need to compute the gradients with respect to.
sourcepub fn constant(c: T) -> Record<'a, T>
pub fn constant(c: T) -> Record<'a, T>
Creates an untracked Record which has no backing WengertList.
This is provided for using constants along with Records in operations.
For example with y = x + 4 the computation graph could be conceived as a y node with parent nodes of x and 4 combined with the operation +. However there is no need to record the derivatives of a constant, so instead the computation graph can be conceived as a y node with a single parent node of x and the unary operation of +4.
This is also used for the type level constructors required by Numeric which are also considered constants.
sourcepub fn variable(x: T, history: &'a WengertList<T>) -> Record<'a, T>
pub fn variable(x: T, history: &'a WengertList<T>) -> Record<'a, T>
Creates a record backed by the provided WengertList.
The record cannot live longer than the WengertList, hence the following example does not compile
use easy_ml::differentiation::Record;
use easy_ml::differentiation::WengertList;
let record = {
let list = WengertList::new();
Record::variable(1.0, &list)
}; // list no longer in scope
You can alternatively use the record constructor on the WengertList type.
sourcepub fn from_existing(
number: (T, Index),
history: Option<&'a WengertList<T>>
) -> Record<'a, T>
pub fn from_existing( number: (T, Index), history: Option<&'a WengertList<T>> ) -> Record<'a, T>
Creates a record from a constant/variable directly, most likely obtained by getting a tensor view of an existing container. The inputs are not checked for validity. It is possible to pass in the wrong Wengert list here or even numbers with indexes that aren’t tracked on the WengertList.
It is recommended to use this constructor only in conjunction with manipulating an existing
container and not for creating new variables. Any variables created outside of
Record::variable
/ RecordContainer::variables
would have to be manually added to the
correct Wengert list, and any arithmetic operations would also need tracking correctly.
sourcepub fn reset(&mut self)
pub fn reset(&mut self)
Resets this Record to place it back on its WengertList, for use in performing another derivation after clearing the WengertList.
sourcepub fn do_reset(x: Record<'_, T>) -> Record<'_, T>
pub fn do_reset(x: Record<'_, T>) -> Record<'_, T>
A convenience helper function which takes a Record by value and calls reset on it.
sourcepub fn history(&self) -> Option<&'a WengertList<T>>
pub fn history(&self) -> Option<&'a WengertList<T>>
Gets the WengertList this Record is backed by if a variable, and None if a constant.
source§impl<'a, T: Numeric + Primitive> Record<'a, T>where
for<'t> &'t T: NumericRef<T>,
impl<'a, T: Numeric + Primitive> Record<'a, T>where
for<'t> &'t T: NumericRef<T>,
sourcepub fn derivatives(&self) -> Derivatives<T>
pub fn derivatives(&self) -> Derivatives<T>
Performs a backward pass up this record’s WengertList from this record as the output, computing all the derivatives for the inputs involving this output.
If you have N inputs x1 to xN, and this output is y, then this computes all the derivatives δy/δxi for i = 1 to N.
§Panics
Panics if the Record has no backing WengertList, ie it was created as a constant.
sourcepub fn try_derivatives(&self) -> Option<Derivatives<T>>
pub fn try_derivatives(&self) -> Option<Derivatives<T>>
Performs a backward pass up this record’s WengertList from this record as the output, computing all the derivatives for the inputs involving this output.
If this record has no WengertList, ie it’s a constant, None is returned instead.
If you have N inputs x1 to xN, and this output is y, then this computes all the derivatives δy/δxi for i = 1 to N.
source§impl<'a, T: Numeric + Primitive> Record<'a, T>where
for<'t> &'t T: NumericRef<T>,
impl<'a, T: Numeric + Primitive> Record<'a, T>where
for<'t> &'t T: NumericRef<T>,
sourcepub fn unary(
&self,
fx: impl Fn(T) -> T,
dfx_dx: impl Fn(T) -> T
) -> Record<'_, T>
pub fn unary( &self, fx: impl Fn(T) -> T, dfx_dx: impl Fn(T) -> T ) -> Record<'_, T>
Creates a new Record from a reference to an existing Record by applying some unary function to it which operates on the type the Record wraps.
To compute the new record, the unary function of some input x to some output y is needed along with its derivative with respect to its input x.
For example, tanh is a commonly used activation function, but the Real trait does not include this operation and Record has no operations for it specifically. However, you can use this function to compute the tanh of a Record like so:
use easy_ml::differentiation::{Record, WengertList};
let list = WengertList::new();
let x = Record::variable(0.7f32, &list);
// the derivative of tanh(x) is sech(x) * sech(x) which is equivalent to
// 1 / (cosh(x) * cosh(x))
let y = x.unary(|x| x.tanh(), |x| 1.0 / (x.cosh() * x.cosh()));
assert_eq!(y.derivatives()[&x], 1.0f32 / (0.7f32.cosh() * 0.7f32.cosh()));
sourcepub fn binary(
&self,
rhs: &Record<'a, T>,
fxy: impl Fn(T, T) -> T,
dfxy_dx: impl Fn(T, T) -> T,
dfxy_dy: impl Fn(T, T) -> T
) -> Record<'_, T>
pub fn binary( &self, rhs: &Record<'a, T>, fxy: impl Fn(T, T) -> T, dfxy_dx: impl Fn(T, T) -> T, dfxy_dy: impl Fn(T, T) -> T ) -> Record<'_, T>
Creates a new Record from a reference to two existing Records by applying some binary function to them which operates on two arguments of the type the Records wrap.
To compute the new record, the binary function of some inputs x and y to some output z is needed along with its derivative with respect to its first input x and its derivative with respect to its second input y.
For example, atan2 takes two arguments, but the Real trait does not include this operation and Record has no operations for it specifically. However, you can use this function to compute the atan2 of two Records like so:
use easy_ml::differentiation::{Record, WengertList};
let list = WengertList::new();
let x = Record::variable(3.0f32, &list);
let y = Record::variable(3.0f32, &list);
// the derivative of atan2 with respect to x is y/(x*x + y*y)
// https://www.wolframalpha.com/input/?i=d%28atan2%28x%2Cy%29%29%2Fdx
// the derivative of atan2 with respect to y is -x/(x*x + y*y)
// https://www.wolframalpha.com/input/?i=d%28atan2%28x%2Cy%29%29%2Fdy
let z = x.binary(&y,
|x, y| x.atan2(y),
|x, y| y/((x*x) + (y*y)),
|x, y| -x/((x*x) + (y*y))
);
let derivatives = z.derivatives();
let dx = derivatives[&x];
let dy = derivatives[&y];
Trait Implementations§
source§impl<'a, 'l, 'r, T: Numeric + Primitive> Add<&'r Record<'a, T>> for &'l Record<'a, T>where
for<'t> &'t T: NumericRef<T>,
impl<'a, 'l, 'r, T: Numeric + Primitive> Add<&'r Record<'a, T>> for &'l Record<'a, T>where
for<'t> &'t T: NumericRef<T>,
Addition for two records of the same type with both referenced and both using the same WengertList.
source§impl<'a, T: Numeric + Primitive> Add<&Record<'a, T>> for Record<'a, T>where
for<'t> &'t T: NumericRef<T>,
impl<'a, T: Numeric + Primitive> Add<&Record<'a, T>> for Record<'a, T>where
for<'t> &'t T: NumericRef<T>,
Operation for two records of the same type with the right referenced.
source§impl<'a, T: Numeric + Primitive> Add<&T> for &Record<'a, T>where
for<'t> &'t T: NumericRef<T>,
impl<'a, T: Numeric + Primitive> Add<&T> for &Record<'a, T>where
for<'t> &'t T: NumericRef<T>,
Addition for a record and a constant of the same type with both referenced.
source§impl<'a, T: Numeric + Primitive> Add<&T> for Record<'a, T>where
for<'t> &'t T: NumericRef<T>,
impl<'a, T: Numeric + Primitive> Add<&T> for Record<'a, T>where
for<'t> &'t T: NumericRef<T>,
Operation for a record and a constant of the same type with the right referenced.
source§impl<'a, T: Numeric + Primitive> Add<Record<'a, T>> for &Record<'a, T>where
for<'t> &'t T: NumericRef<T>,
impl<'a, T: Numeric + Primitive> Add<Record<'a, T>> for &Record<'a, T>where
for<'t> &'t T: NumericRef<T>,
Operation for two records of the same type with the left referenced.
source§impl<'a, T: Numeric + Primitive> Add<T> for &Record<'a, T>where
for<'t> &'t T: NumericRef<T>,
impl<'a, T: Numeric + Primitive> Add<T> for &Record<'a, T>where
for<'t> &'t T: NumericRef<T>,
Operation for a record and a constant of the same type with the left referenced.
source§impl<'a, T: Numeric + Primitive> Add<T> for Record<'a, T>where
for<'t> &'t T: NumericRef<T>,
impl<'a, T: Numeric + Primitive> Add<T> for Record<'a, T>where
for<'t> &'t T: NumericRef<T>,
Operation for a record and a constant of the same type.
source§impl<'a, T: Numeric + Primitive> Add for Record<'a, T>where
for<'t> &'t T: NumericRef<T>,
impl<'a, T: Numeric + Primitive> Add for Record<'a, T>where
for<'t> &'t T: NumericRef<T>,
Operation for two records of the same type.
source§impl<'a, T: Clone + Primitive> Clone for Record<'a, T>
impl<'a, T: Clone + Primitive> Clone for Record<'a, T>
Any record of a Cloneable type implements clone
source§impl<'a, T: Numeric + Real + Primitive> Cos for &Record<'a, T>
impl<'a, T: Numeric + Real + Primitive> Cos for &Record<'a, T>
Cosine of a Record by reference.
source§impl<'a, T: Numeric + Real + Primitive> Cos for Record<'a, T>
impl<'a, T: Numeric + Real + Primitive> Cos for Record<'a, T>
Operation for a record by value.
source§impl<'a, T: Display + Primitive> Display for Record<'a, T>
impl<'a, T: Display + Primitive> Display for Record<'a, T>
A record is displayed by showing its number component.
source§impl<'a, 'l, 'r, T: Numeric + Primitive> Div<&'r Record<'a, T>> for &'l Record<'a, T>where
for<'t> &'t T: NumericRef<T>,
impl<'a, 'l, 'r, T: Numeric + Primitive> Div<&'r Record<'a, T>> for &'l Record<'a, T>where
for<'t> &'t T: NumericRef<T>,
Dvision for two records of the same type with both referenced and both using the same WengertList.
source§impl<'a, T: Numeric + Primitive> Div<&Record<'a, T>> for Record<'a, T>where
for<'t> &'t T: NumericRef<T>,
impl<'a, T: Numeric + Primitive> Div<&Record<'a, T>> for Record<'a, T>where
for<'t> &'t T: NumericRef<T>,
Operation for two records of the same type with the right referenced.
source§impl<'a, T: Numeric + Primitive> Div<&T> for &Record<'a, T>where
for<'t> &'t T: NumericRef<T>,
impl<'a, T: Numeric + Primitive> Div<&T> for &Record<'a, T>where
for<'t> &'t T: NumericRef<T>,
Division for a record and a constant of the same type with both referenced.
source§impl<'a, T: Numeric + Primitive> Div<&T> for Record<'a, T>where
for<'t> &'t T: NumericRef<T>,
impl<'a, T: Numeric + Primitive> Div<&T> for Record<'a, T>where
for<'t> &'t T: NumericRef<T>,
Operation for a record and a constant of the same type with the right referenced.
source§impl<'a, T: Numeric + Primitive> Div<Record<'a, T>> for &Record<'a, T>where
for<'t> &'t T: NumericRef<T>,
impl<'a, T: Numeric + Primitive> Div<Record<'a, T>> for &Record<'a, T>where
for<'t> &'t T: NumericRef<T>,
Operation for two records of the same type with the left referenced.
source§impl<'a, T: Numeric + Primitive> Div<T> for &Record<'a, T>where
for<'t> &'t T: NumericRef<T>,
impl<'a, T: Numeric + Primitive> Div<T> for &Record<'a, T>where
for<'t> &'t T: NumericRef<T>,
Operation for a record and a constant of the same type with the left referenced.
source§impl<'a, T: Numeric + Primitive> Div<T> for Record<'a, T>where
for<'t> &'t T: NumericRef<T>,
impl<'a, T: Numeric + Primitive> Div<T> for Record<'a, T>where
for<'t> &'t T: NumericRef<T>,
Operation for a record and a constant of the same type.
source§impl<'a, T: Numeric + Primitive> Div for Record<'a, T>where
for<'t> &'t T: NumericRef<T>,
impl<'a, T: Numeric + Primitive> Div for Record<'a, T>where
for<'t> &'t T: NumericRef<T>,
Operation for two records of the same type.
source§impl<'a, T: Numeric + Real + Primitive> Exp for &Record<'a, T>
impl<'a, T: Numeric + Real + Primitive> Exp for &Record<'a, T>
Exponential, ie ex of a Record by reference.
source§impl<'a, T: Numeric + Real + Primitive> Exp for Record<'a, T>
impl<'a, T: Numeric + Real + Primitive> Exp for Record<'a, T>
Operation for a record by value.
source§impl<'a, T> From<&Record<'a, T>> for RecordTensor<'a, T, Tensor<(T, Index), 0>, 0>
impl<'a, T> From<&Record<'a, T>> for RecordTensor<'a, T, Tensor<(T, Index), 0>, 0>
A record can be converted losslessly into a zero dimensional record tensor.
source§impl<'a, T, S> From<&RecordContainer<'a, T, TensorView<(T, usize), S, 0>, 0>> for Record<'a, T>
impl<'a, T, S> From<&RecordContainer<'a, T, TensorView<(T, usize), S, 0>, 0>> for Record<'a, T>
A zero dimensional record tensor can be converted losslessly into a record.
source§fn from(scalar: &RecordTensor<'a, T, S, 0>) -> Record<'a, T>
fn from(scalar: &RecordTensor<'a, T, S, 0>) -> Record<'a, T>
Converts the sole element in the zero dimensional record tensor into a record.
source§impl<'a, T> From<Record<'a, T>> for RecordTensor<'a, T, Tensor<(T, Index), 0>, 0>
impl<'a, T> From<Record<'a, T>> for RecordTensor<'a, T, Tensor<(T, Index), 0>, 0>
A record can be converted losslessly into a zero dimensional record tensor.
source§impl<'a, T, S> From<RecordContainer<'a, T, TensorView<(T, usize), S, 0>, 0>> for Record<'a, T>
impl<'a, T, S> From<RecordContainer<'a, T, TensorView<(T, usize), S, 0>, 0>> for Record<'a, T>
A zero dimensional record tensor can be converted losslessly into a record.
source§fn from(scalar: RecordTensor<'a, T, S, 0>) -> Record<'a, T>
fn from(scalar: RecordTensor<'a, T, S, 0>) -> Record<'a, T>
Converts the sole element in the zero dimensional record tensor into a record.
source§impl<'a, T: Numeric + Real + Primitive> Ln for &Record<'a, T>
impl<'a, T: Numeric + Real + Primitive> Ln for &Record<'a, T>
Natural logarithm, ie ln(x) of a Record by reference.
source§impl<'a, 'l, 'r, T: Numeric + Primitive> Mul<&'r Record<'a, T>> for &'l Record<'a, T>where
for<'t> &'t T: NumericRef<T>,
impl<'a, 'l, 'r, T: Numeric + Primitive> Mul<&'r Record<'a, T>> for &'l Record<'a, T>where
for<'t> &'t T: NumericRef<T>,
Multiplication for two records of the same type with both referenced and both using the same WengertList.
source§impl<'a, T: Numeric + Primitive> Mul<&Record<'a, T>> for Record<'a, T>where
for<'t> &'t T: NumericRef<T>,
impl<'a, T: Numeric + Primitive> Mul<&Record<'a, T>> for Record<'a, T>where
for<'t> &'t T: NumericRef<T>,
Operation for two records of the same type with the right referenced.
source§impl<'a, T: Numeric + Primitive> Mul<&T> for &Record<'a, T>where
for<'t> &'t T: NumericRef<T>,
impl<'a, T: Numeric + Primitive> Mul<&T> for &Record<'a, T>where
for<'t> &'t T: NumericRef<T>,
Multiplication for a record and a constant of the same type with both referenced.
source§impl<'a, T: Numeric + Primitive> Mul<&T> for Record<'a, T>where
for<'t> &'t T: NumericRef<T>,
impl<'a, T: Numeric + Primitive> Mul<&T> for Record<'a, T>where
for<'t> &'t T: NumericRef<T>,
Operation for a record and a constant of the same type with the right referenced.
source§impl<'a, T: Numeric + Primitive> Mul<Record<'a, T>> for &Record<'a, T>where
for<'t> &'t T: NumericRef<T>,
impl<'a, T: Numeric + Primitive> Mul<Record<'a, T>> for &Record<'a, T>where
for<'t> &'t T: NumericRef<T>,
Operation for two records of the same type with the left referenced.
source§impl<'a, T: Numeric + Primitive> Mul<T> for &Record<'a, T>where
for<'t> &'t T: NumericRef<T>,
impl<'a, T: Numeric + Primitive> Mul<T> for &Record<'a, T>where
for<'t> &'t T: NumericRef<T>,
Operation for a record and a constant of the same type with the left referenced.
source§impl<'a, T: Numeric + Primitive> Mul<T> for Record<'a, T>where
for<'t> &'t T: NumericRef<T>,
impl<'a, T: Numeric + Primitive> Mul<T> for Record<'a, T>where
for<'t> &'t T: NumericRef<T>,
Operation for a record and a constant of the same type.
source§impl<'a, T: Numeric + Primitive> Mul for Record<'a, T>where
for<'t> &'t T: NumericRef<T>,
impl<'a, T: Numeric + Primitive> Mul for Record<'a, T>where
for<'t> &'t T: NumericRef<T>,
Operation for two records of the same type.
source§impl<'a, T: Numeric + Primitive> Neg for &Record<'a, T>where
for<'t> &'t T: NumericRef<T>,
impl<'a, T: Numeric + Primitive> Neg for &Record<'a, T>where
for<'t> &'t T: NumericRef<T>,
Negation of a record by reference.
source§impl<'a, T: Numeric + Primitive> Neg for Record<'a, T>where
for<'t> &'t T: NumericRef<T>,
impl<'a, T: Numeric + Primitive> Neg for Record<'a, T>where
for<'t> &'t T: NumericRef<T>,
Negation of a record by value.
source§impl<'a, T: PartialEq + Primitive> PartialEq for Record<'a, T>
impl<'a, T: PartialEq + Primitive> PartialEq for Record<'a, T>
Any record of a PartialEq type implements PartialEq
Note that as a Record is intended to be substitutable with its type T only the number parts of the record are compared.
source§impl<'a, T: PartialOrd + Primitive> PartialOrd for Record<'a, T>
impl<'a, T: PartialOrd + Primitive> PartialOrd for Record<'a, T>
Any record of a PartialOrd type implements PartialOrd
Note that as a Record is intended to be substitutable with its type T only the number parts of the record are compared.
1.0.0 · source§fn le(&self, other: &Rhs) -> bool
fn le(&self, other: &Rhs) -> bool
self
and other
) and is used by the <=
operator. Read moresource§impl<'a, 'l, 'r, T: Numeric + Real + Primitive> Pow<&'r Record<'a, T>> for &'l Record<'a, T>
impl<'a, 'l, 'r, T: Numeric + Real + Primitive> Pow<&'r Record<'a, T>> for &'l Record<'a, T>
Power of one Record to another, ie self^rhs for two records of the same type with both referenced and both using the same WengertList.
source§impl<'a, T: Numeric + Real + Primitive> Pow<&Record<'a, T>> for &T
impl<'a, T: Numeric + Real + Primitive> Pow<&Record<'a, T>> for &T
Power of a constant to a Record of the same type with both referenced.
source§impl<'a, T: Numeric + Real + Primitive> Pow<&Record<'a, T>> for Record<'a, T>
impl<'a, T: Numeric + Real + Primitive> Pow<&Record<'a, T>> for Record<'a, T>
Operation for two records of the same type with the right referenced.
source§impl<'a, T: Numeric + Real + Primitive> Pow<&Record<'a, T>> for T
impl<'a, T: Numeric + Real + Primitive> Pow<&Record<'a, T>> for T
Operation for a constant and a record of the same type with the right referenced.
source§impl<'a, T: Numeric + Real + Primitive> Pow<&T> for &Record<'a, T>
impl<'a, T: Numeric + Real + Primitive> Pow<&T> for &Record<'a, T>
Power of one Record to a constant of the same type with both referenced.
source§impl<'a, T: Numeric + Real + Primitive> Pow<&T> for Record<'a, T>
impl<'a, T: Numeric + Real + Primitive> Pow<&T> for Record<'a, T>
Operation for a record and a constant of the same type with the right referenced.
source§impl<'a, T: Numeric + Real + Primitive> Pow<Record<'a, T>> for &Record<'a, T>
impl<'a, T: Numeric + Real + Primitive> Pow<Record<'a, T>> for &Record<'a, T>
Operation for two records of the same type with the left referenced.
source§impl<'a, T: Numeric + Real + Primitive> Pow<Record<'a, T>> for &T
impl<'a, T: Numeric + Real + Primitive> Pow<Record<'a, T>> for &T
Operation for a constant and a record of the same type with the left referenced.
source§impl<'a, T: Numeric + Real + Primitive> Pow<Record<'a, T>> for T
impl<'a, T: Numeric + Real + Primitive> Pow<Record<'a, T>> for T
Operation for a constant and a record of the same type.
source§impl<'a, T: Numeric + Real + Primitive> Pow<T> for &Record<'a, T>
impl<'a, T: Numeric + Real + Primitive> Pow<T> for &Record<'a, T>
Operation for a record and a constant of the same type with the left referenced.
source§impl<'a, T: Numeric + Real + Primitive> Pow<T> for Record<'a, T>
impl<'a, T: Numeric + Real + Primitive> Pow<T> for Record<'a, T>
Operation for a record and a constant of the same type.
source§impl<'a, T: Numeric + Real + Primitive> Pow for Record<'a, T>
impl<'a, T: Numeric + Real + Primitive> Pow for Record<'a, T>
Operation for two records of the same type.
source§impl<'a, T: Numeric + Real + Primitive> Sin for Record<'a, T>
impl<'a, T: Numeric + Real + Primitive> Sin for Record<'a, T>
Operation for a record by value.
source§impl<'a, T: Numeric + Real + Primitive> Sqrt for &Record<'a, T>
impl<'a, T: Numeric + Real + Primitive> Sqrt for &Record<'a, T>
Square root of a Record by reference.
source§impl<'a, T: Numeric + Real + Primitive> Sqrt for Record<'a, T>
impl<'a, T: Numeric + Real + Primitive> Sqrt for Record<'a, T>
Operation for a record by value.
source§impl<'a, 'l, 'r, T: Numeric + Primitive> Sub<&'r Record<'a, T>> for &'l Record<'a, T>where
for<'t> &'t T: NumericRef<T>,
impl<'a, 'l, 'r, T: Numeric + Primitive> Sub<&'r Record<'a, T>> for &'l Record<'a, T>where
for<'t> &'t T: NumericRef<T>,
Subtraction for two records of the same type with both referenced and both using the same WengertList.
source§impl<'a, T: Numeric + Primitive> Sub<&Record<'a, T>> for Record<'a, T>where
for<'t> &'t T: NumericRef<T>,
impl<'a, T: Numeric + Primitive> Sub<&Record<'a, T>> for Record<'a, T>where
for<'t> &'t T: NumericRef<T>,
Operation for two records of the same type with the right referenced.
source§impl<'a, T: Numeric + Primitive> Sub<&T> for &Record<'a, T>where
for<'t> &'t T: NumericRef<T>,
impl<'a, T: Numeric + Primitive> Sub<&T> for &Record<'a, T>where
for<'t> &'t T: NumericRef<T>,
Subtraction for a record and a constant of the same type with both referenced.
source§impl<'a, T: Numeric + Primitive> Sub<&T> for Record<'a, T>where
for<'t> &'t T: NumericRef<T>,
impl<'a, T: Numeric + Primitive> Sub<&T> for Record<'a, T>where
for<'t> &'t T: NumericRef<T>,
Operation for a record and a constant of the same type with the right referenced.
source§impl<'a, T: Numeric + Primitive> Sub<Record<'a, T>> for &Record<'a, T>where
for<'t> &'t T: NumericRef<T>,
impl<'a, T: Numeric + Primitive> Sub<Record<'a, T>> for &Record<'a, T>where
for<'t> &'t T: NumericRef<T>,
Operation for two records of the same type with the left referenced.
source§impl<'a, T: Numeric + Primitive> Sub<T> for &Record<'a, T>where
for<'t> &'t T: NumericRef<T>,
impl<'a, T: Numeric + Primitive> Sub<T> for &Record<'a, T>where
for<'t> &'t T: NumericRef<T>,
Operation for a record and a constant of the same type with the left referenced.
source§impl<'a, T: Numeric + Primitive> Sub<T> for Record<'a, T>where
for<'t> &'t T: NumericRef<T>,
impl<'a, T: Numeric + Primitive> Sub<T> for Record<'a, T>where
for<'t> &'t T: NumericRef<T>,
Operation for a record and a constant of the same type.
source§impl<'a, T: Numeric + Primitive> Sub for Record<'a, T>where
for<'t> &'t T: NumericRef<T>,
impl<'a, T: Numeric + Primitive> Sub for Record<'a, T>where
for<'t> &'t T: NumericRef<T>,
Operation for two records of the same type.
source§impl<'a, T: Numeric + Primitive> Sum for Record<'a, T>
impl<'a, T: Numeric + Primitive> Sum for Record<'a, T>
Any record of a Numeric type implements Sum, which is the same as adding a bunch of Record types together.
source§impl<'a, T: Numeric + Primitive> SwappedOperations<&T> for &Record<'a, T>where
for<'t> &'t T: NumericRef<T>,
impl<'a, T: Numeric + Primitive> SwappedOperations<&T> for &Record<'a, T>where
for<'t> &'t T: NumericRef<T>,
source§fn sub_swapped(self, lhs: &T) -> Self::Output
fn sub_swapped(self, lhs: &T) -> Self::Output
Subtraction for a record and a constant, where the constant is the left hand side, ie C - record.
source§fn div_swapped(self, lhs: &T) -> Self::Output
fn div_swapped(self, lhs: &T) -> Self::Output
Division for a record and a constant, where the constant is the left hand side, ie C / record.
type Output = Record<'a, T>
source§impl<'a, T: Numeric + Primitive> SwappedOperations<&T> for Record<'a, T>where
for<'t> &'t T: NumericRef<T>,
impl<'a, T: Numeric + Primitive> SwappedOperations<&T> for Record<'a, T>where
for<'t> &'t T: NumericRef<T>,
source§fn sub_swapped(self, lhs: &T) -> Self::Output
fn sub_swapped(self, lhs: &T) -> Self::Output
Subtraction for a record and a constant, where the constant is the left hand side, ie C - record.
source§fn div_swapped(self, lhs: &T) -> Self::Output
fn div_swapped(self, lhs: &T) -> Self::Output
Division for a record and a constant, where the constant is the left hand side, ie C / record.
type Output = Record<'a, T>
source§impl<'a, T: Numeric + Primitive> SwappedOperations<T> for &Record<'a, T>where
for<'t> &'t T: NumericRef<T>,
impl<'a, T: Numeric + Primitive> SwappedOperations<T> for &Record<'a, T>where
for<'t> &'t T: NumericRef<T>,
source§fn sub_swapped(self, lhs: T) -> Self::Output
fn sub_swapped(self, lhs: T) -> Self::Output
Subtraction for a record and a constant, where the constant is the left hand side, ie C - record.
source§fn div_swapped(self, lhs: T) -> Self::Output
fn div_swapped(self, lhs: T) -> Self::Output
Division for a record and a constant, where the constant is the left hand side, ie C / record.
type Output = Record<'a, T>
source§impl<'a, T: Numeric + Primitive> SwappedOperations<T> for Record<'a, T>where
for<'t> &'t T: NumericRef<T>,
impl<'a, T: Numeric + Primitive> SwappedOperations<T> for Record<'a, T>where
for<'t> &'t T: NumericRef<T>,
source§fn sub_swapped(self, lhs: T) -> Self::Output
fn sub_swapped(self, lhs: T) -> Self::Output
Subtraction for a record and a constant, where the constant is the left hand side, ie C - record.
source§fn div_swapped(self, lhs: T) -> Self::Output
fn div_swapped(self, lhs: T) -> Self::Output
Division for a record and a constant, where the constant is the left hand side, ie C / record.
type Output = Record<'a, T>
source§impl<'a, T: Numeric + Primitive> ZeroOne for Record<'a, T>
impl<'a, T: Numeric + Primitive> ZeroOne for Record<'a, T>
Record implements ZeroOne by returning constants.
impl<'a, T: Copy + Primitive> Copy for Record<'a, T>
Any record of a Copy type implements Copy